Moduli Axions, Stabilizing Moduli and the Large Field Swampland Conjecture in Heterotic M-Theory

We compute the potential energy for the dilaton, complex structure and Kahler moduli and search of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds. We present a protocol for deriving the potential that combines the non-perturbative complex structure, gaugino condensate and worldsheet instanton superpotentials in theories in which the hidden sector contains an anomalous $U(1)$ structure group. The Green-Schwarz anomaly cancellation induces inhomogeneous axion transformations for the imaginary components of the dilaton and Kahler modulus. Using this protocol we obtain explicit examples in which potential has a global minimum at negative or zero vacuum density or a metastable minimum with positive vacuum density. In all three cases, the dilaton, Kahler modulus and associated axion moduli are completely stabilized. Finally, we show that, for any of these vacua, the potential energy satisfies the large scalar field Swampland conjecture.